The problem involves locating relative maxima, minima, and saddle points for the function f(x,y) = x² + xy + y² - 3x. Participants are working through the critical points and the second derivative test.
Some participants have provided guidance on the correct formula for the determinant used in the second derivative test. There is ongoing clarification about the mixed second derivative and its calculation.
Participants express uncertainty about specific calculations and the definitions of derivatives involved in the problem. There is mention of a discrepancy in expected values during the evaluation of the function at critical points.
Mdhiggenz said:Homework Statement
Locate all relative max,min,and saddle points if any.
f(x,y)=x2+xy+y2-3x
fx=2x+y-3
fy=x+2y
Skipping some algebra I get the critical points (2,-1)
fxx=2
fyy=2
d=fxx*fyy-f(x0,y0)2
d=4-9=-5
I know I'm messing up at f(x0,y0)
I'm simply plugging in my c.p points (2,-1) into
f(x,y)=x2+xy+y2-3x
but seem to keep getting -3
While the value 1 is suppose to come out
Homework Equations
The Attempt at a Solution
Mdhiggenz said:I'm a bit confused what do you mean mixed second derivative?